Abstract
In this paper we consider r-dominating cliques in homogeneously orderable graphs (a common generalization of dually chordal and distancehereditary graphs) and their relation to strict r-packing sets. We give a simple criterion for the existence of r-dominating clique and show that the cardinality of a maximum strict r-packing set equals the cardinality of a minimum r-dominating clique provided the last parameter exists and is not two. Finally we present two efficient algorithms. The first one decides whether a given homogeneously orderable graph has a r-dominating clique and, if so, computes both a minimum r-dominating clique and a maximum strict r-packing set of the graph. The second one computes a minimum connected r-dominating set in this graph.
First author supported by DAAD. Second author supported by DFG.
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© 1995 Springer-Verlag Berlin Heidelberg
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Dragan, F.F., Nicolai, F. (1995). r-Domination problems on homogeneously orderable graphs. In: Reichel, H. (eds) Fundamentals of Computation Theory. FCT 1995. Lecture Notes in Computer Science, vol 965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60249-6_52
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DOI: https://doi.org/10.1007/3-540-60249-6_52
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